Statistical thinking — probability distributions
2024-09-19
The simplest experiment has two outcomes; success or failure
In statistics observations such observations follow a Bernoulli distribution
If we tossed a fair coin ten times, we might observe
Each individual trial (coin toss) is a Bernoulli random variable
A binomial random variable is the number of successful results in \(n\) independent Bernoulli trials
We tossed the coin ten times, hence we had n = 10 trials
If we treat Heads as success we saw 6 successes
This number is a binomial count
20 coin tosses, repeated 100 times
How many heads do we see in each trial?
A Poisson random variable is the number of occurrences of an event recorded in a sample of fixed area or time
Single parameter, \(\lambda\), is the rate parameter or Poisson mean, the mean number of occurrences of events in each sample
Many environmental variables can not be described by discrete variables
Continuous random variables can take on any value, perhaps bounded by an interval with appropriate upper and lower limits
The precision of a measured value of a continuous random variable is limited by the available instrumentation
Bell curve is a familiar probability distribution — known as the normal or Gaussian
Many observations clustered about the central or average value, observations extending into the tails.